Critical analysis and extension of the Nodal Expansion Method for the spatial discretization of the neutron diffusion equation
The Nodal Expansion Method (NEM) for the spatial discretization of the neutron diffusion equation is critically examined. Techniques are presented which facilitate the determination of the acceptable local support of polynomial expansions of the neutron flux. The allowable patterns of support for several classes of expansions are ascertained. Methods are developed for the addition of both one-dimensional and multidimensional trial functions to a quadratic variant of the NEM. Several weighted residual methods for defining the coefficients of cubic and higher order, one-dimensional trial functions are described. The biquadratic expansion is used as the basis for the development of two nodal methods which employ multidimensional trial functions. The concurrent inclusion of both multidimensional and high order one-dimensional trial functions is accomplished by means of noniterative techniques, which are applied subsequent to the completion of a lower order NEM computation. The effects upon the accuracy of both local and global parameters, of the addition of one-dimensional and multidimensional trial functions to the two-dimensional flux expansion (in one energy group) using these techniques, are examined. Finally, application of the advances in NEM technology to polar geometry is documented.
- Research Organization:
- Virginia Univ., Charlottesville (USA)
- OSTI ID:
- 5576156
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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